Not that I'm advocating gambling, but River Rock Casino may have dining options open later than a stand-alone restaurant. It's been a while since I've visited there, but it's relatively close to your hotel that the cab ride shouldn't be terribly expensive. (I'm guessing $10-15 each way (I find Richmond traffic is terrible), so should be cheaper than renting a car, plus parking fees at hotel.)
Since you're headed to TPE where you can get your fill of Taiwanese/Chinese cuisine, the casino will at least offer some other options (burgers / pizza, etc). I'm not sure if the "fine dining" options will still be open though.